MicroeconomiaCorso E

John Hey

Compito a casa/Homework

• CES technology with parameters c1=0.4, c2=0.5, ρ=0.9 and s=1.0.

• The production function:• y = ((0.4q1

-0.9)+(0.5q2-0.9))-1/0.9

• I have inserted the isoquant for output = 40 (and also that for output=60).

• I have inserted the lowest isocost at the prices w1 = 1 and w2 = 1 for the inputs.

• The optimal combination: q1 = 33.38 q2 = 37.54• and the cost = 33.58+37.54 = 70.92.

What you should do

• Find the optimal combination (either graphically or otherwise) and the (minimum) cost to produce the output for the following:

• w1 = 2 w2 = 1 y=40

• w1 = 3 w2 = 1 y=40

• w1 = 1 w2 = 1 y=60

• w1 = 2 w2 = 1 y=60

• w1 = 3 w2 = 1 y=60

• Put the results in a table.

Results

y w1 w2 q1 q2 costo

40 1 1 32.4 37.5 70.9

40 2 1 27.9 45.2 101.1

40 3 1 25.5 51.2 127.7

60 1 1 50.1 56.3 106.4

60 2 1 41.9 67.9 151.7

60 3 1 38.3 76.7 191.6

Chapter 12

• The total cost C(y) is the minimum cost to produce a given level of output y.

• It is always upward-sloping (in the long period passes through the origin) and its shape depends upon the returns to scale:

• decreasing ↔ convex• constant ↔ linear• increasing ↔ concave

Chapter 12

• The total cost C(y) is the minimum cost to produce a given level of output y.

• The average cost = C(y)/y – is the slope of the line from the origin to the total cost curve.

• The marginal cost – the rate at which total cost increases with output – is equal to the slope of the total cost curve.

Constant returns to scaleTotal cost

Constant returns to scaleMarginal cost

Decreasing returns to scaleTotal cost

Two examples

Average cost at an output of 40

Average cost at the output of 80

The average cost curve

Marginal cost at the output 40

Marginal cost at the output 80

The marginal cost curve

From the total cost curve to the marginal cost curve and back.

• The marginal cost curve is the slope of the total cost curve...

• ... hence the total cost curve is the area under the marginal cost curve.

• The marginal cost curve is the derivative of the total cost curve...

• ... hence the total cost curve is the integral of the marginal cost curve.

Constant returns to scale

Constant returns to scale

Decreasing returns to scale

Decreasing returns to scale

Chapter 13

• Today we find the optimal output for a perfectly competitive firm...

• ...that takes the price of its output as given.

• We will assume to begin with that the firm has decreasing returns to scale.

• We will see later that there are problems if the firm has increasing returns to scale.

Chapter 13

• We use the following notation:• y for the level of output.• p for the price of the output.• C(y) for the total (minimum) cost to produce a

level of output y.• We find the condition for the optimal output of

the firm and hence its supply curve.• We prove a familiar result about the

profits/surplus of the firm.

Chapter 13

• The condition for the optimal output:

• p = marginal cost...

• ... where marginal cost is rising.

• It follows that the supply curve of the firm is simply its marginal cost curve.

• The profit/surplus of the firm is the area between the price and its supply curve.

Chapter 13

• Goodbye!